In a certain game, each of 5 players received a score between 0 and 100, inclusive. If their average (arithmetic mean) score was 80, what is the greatest possible number of the 5 players who could have received a score of 50? Explain.

Question

(A)None
(B)One
(C)Two

The average is defined this way:

average=1/5 (score1 + score2 + ...)

Here. We want to find the number n of folks that can get a 50 with a class average of 80.

80=1/5(n*50 + sum of other scores)

Now, to maximize n, we need to maximize the sum of the other scores, or
80=1/5(n*50 + 100*(5-n))
solve for n